I don't know if you took your child to a pediatrician or an eye doctor (optometrist or ophthalmologist), but if you haven't taken her to an eye doctor please do so. Regular doctors only talked about eyes for two days in medical school (I was shocked to find that out too) so they are very bad at treating anything with the eye, even pink eye. If you took her to her pediatrician she may have been given an incorrect diagnosis or an inappropriate antibiotic.
I just noticed some comments about a breast milk remedy. It does sound crazy, but I know it can clear a plugged tear duct in a baby so it may work on an infection as well. My husband is an eye doctor and while he was in school (just a few years ago) the baby of one of the other student's had a really stubborn clogged tear duct. They tried putting breast milk in his eye and it cleared right up. He asked one of the professors in class about it the next day and he said it is a known, verified, and effective treatment for unclogging a tear duct in a baby. I just asked my husband about using it on an eye infection and he said he hadn't heard anything about that, but it's worth a shot.